Many NMR procedures and tests such as MRI, volume selective excitation, diffusion, and fluid flow use gradient magnetic fields which must to be linear over large volumes and which have to be switched on and off rapidly. Typically, cylindrical shapes are used for the coils which generate these gradient magnetic fields. For example, a simple gradient coil set that generates x, y and z gradients can be wound on a cylinder of radius R and is made up of a Maxwell coil and two sets of saddle coils as is described in P. G. Morris, "Nuclear Magnetic Resonance Imaging in Medicine and Biology", Clarendon Press, Oxford, 1986. The volume within this cylinder over which the gradients are satisfactorily linear (i.e. the effective volume), however, is less than a sphere of radius 0.6 R due to the small number of wire positions used to construct the coils. This effective volume can be enlarged into a cylinder of radius R and having an arbitrary length by using a distributed filamentary winding on the surface of the cylinder which approximates a continuous current distribution.
Surrounding the gradient coil set are metallic structures such as dewars, magnet coil forms, or magnet windings in which the time dependent fringing field of the gradient coils generate eddy currents. The magnetic fields produced by the eddy currents distort the time dependence and spatial dependence of the gradient field within the gradient coil set. A second set of actively driven coils surrounds the original gradient set to shield the coils and thereby reduce the size of the fringing field. One such coil system for producing a linear gradient magnetic field in a cylinder is described in U.S. Pat. No. 4,737,716. Another cylindrical gradient system is shown in U.S. Pat. No. 4,646,024.
The techniques proposed in these references for producing linear gradients over large volumes and actively shielding them are based upon placing the gradient windings on long concentric cylinders. This is an attractive configuration because of the cylindrical symmetry of the superconducting magnets and the ease of inserting and removing of probes, samples, and specimens. However, the open ends of the cylindrical coils generate "end effects" on the gradient fields inside the cylinders, and thus create, non-uniformities in the gradient. There are also "end effects" that affect the shape of the fringing fields, thereby making it difficult to design the second set of coils required to shield the fringing field.
U.S. Pat. Nos. 3,566,255 and 3,582,779 disclose the use of a set of five or seven independent coil loops having different configurations which improve the homogeneity of certain magnetic fields by removing certain undesired first and second order gradients. The five coil set removes the first order gradients and the seven coil set removes the second order gradients. The figures in these patents show the different sets of coil configurations needed for a sphere and a cube. These coil configurations are described as being particularly useful where the gyromagnetic resonance of a sample is being measured for spectroscopy purposes or for measuring the magnitude of the magnetic field produced by the sample therein.
These patents do not show a coil system wherein the magnetic field outside the coil system is negligiable. Moreover, the coil system requires a set of five or even independent current loops wherein wires cross the equator of the sphere or cube.
It would be desirable, therefore, to develop a simple distributed coil system for generating a linear gradient magnetic field wherein these "end effects" and fringing fields did not present the problems described above.